Do you have a Summary Plan Description for your health insurance? That will give you the breakdown of what the insurance pays and what you pay, generally. Like an Office Visit the plan will pay 80% and the patient will pay 20% subject (or not) to a deductible.
If you have not been given one, you should ask for one.
Also, maybe you could ask your insurance company the percentage the plan pays for the type of service (surgery center) that will at least give you a rough estimate of the cost.
Good luck kiddo, dealing with insurance companies is not fun.